I have to disagree with the statement about 3PH backhoes breaking tractors. I just don't buy that a properly rigged 3PH BH is any more at risk of breaking either the BH or tractor than any other mount.
ALL of the kubota BHs are 3ph mount except for the
B21/35/45 series. There is no way they would not be engineered to be safe and servicable.
It IS essential to check with the tractor manufacturer to see if the use of a 3PH BH is supported, and to understand what accessories are required for proper rigging. Some of the smaller kubota's, for example, require the addition of braces and reinforced upper 3PH brackets to support a 3PH BH, but once they are installed it's absolutely fine to use it.
It IS essential to not fit too large a BH to a tractor. That could cause structural failure regardless of the mount. Check with the tractor and BH manufacturer to get their recommended BH sizes for your tractor.
I think the choice between a "frame" mount and a 3PH mount should be made on the real differences where they really exist. For example, the original poster asked about switching between BH and belly mower. With the smaller kubota's (not sure about the 3010), a woods BH with "frame" is NOT compatible with a belly mower. You have to unbolt and rebolt various sub-frame brackets etc. to switch between the two. That's a real basis for choosing between the two. A dismounted "frame" BH (like a woods) has a frame that sticks out 4-5 feet and takes up more storage space. This could be a significant factor in choosing.
I can't comment first hand on which is faster to install/remove because I've only done one of them, but from looking at them I can believe that a "frame" mount could be faster to install/remove than a 3PH. I can also believe that a "frame" mount will allow less movement between the BH and tractor when operating than a 3PH. Depending on your values, these may or may not be significant factors.
I don't mean to get religious about this, but I think it's most important to pick based on the real differences, and as always be sure you rig your tractor properly for whatever attachment you use.
Peter